Gradiometric parallel superconducting quantum interface device

ABSTRACT

Techniques regarding parallel gradiometric SQUIDs and the manufacturing thereof are provided. For example, one or more embodiments described herein can comprise an apparatus, which can comprise a first pattern of superconducting material located on a substrate. Also, the apparatus can comprise a second pattern of superconducting material that can extend across the first pattern of superconducting material at a position. Further, the apparatus can comprise a Josephson junction located at the position, which can comprise an insulating barrier that can connect the first pattern of superconductor material and the second pattern of superconductor material.

BACKGROUND

The subject disclosure relates to a gradiometric parallelsuperconducting quantum interface device, and more specifically, to agradiometric parallel superconducting quantum interface device that canbe suitable for frequency tuning of superconducting quantum bits.

Many different types of superconducting devices regard superconductingquantum interference device (“SQUID”) technology. The critical currentof a SQUID can be tuned by applying a magnetic flux to the loop of theSQUID. The relation between magnetic flux and the critical current is ofgreat importance in several applications such as, in magnetometers andin frequency tuning of superconducting microwave devices (e.g.,resonators and quantum bits).

The very high sensitivity to magnetic flux can also be a disadvantagefor qubit applications since fluctuations can lead to qubit dephasing.By utilizing a gradiometric design, fluctuations in the absolute globalmagnetic field can be eliminated and only fluctuations in the magneticfield gradient will lead to dephasing. Conventional gradiometric SQUIDdesign comprises twisting a direct current (“DC”) SQUID loop such thatthe loop crosses over itself and thereby creates two loops and twomagnetic fluxes. Typically, to separate the electrodes a dielectricmaterial is deposited at the crossover location in the gradiometricdesign. However, said positioning of the dielectric material cannegatively affect the performance of superconducting quantum bits;thereby limiting the applications of conventional gradiometric SQUIDs.

SUMMARY

The following presents a summary to provide a basic understanding of oneor more embodiments of the invention. This summary is not intended toidentify key or critical elements, or delineate any scope of theparticular embodiments or any scope of the claims. Its sole purpose isto present concepts in a simplified form as a prelude to the moredetailed description that is presented later. In one or more embodimentsdescribed herein, apparatuses and/or methods regarding parallelgradiometric SQUIDs are described.

According to an embodiment, an apparatus is provided. The apparatus cancomprise a first pattern of superconducting material located on asubstrate. Also, the apparatus can comprise a second pattern ofsuperconducting material that can extend across the first pattern ofsuperconducting material at a position. Further, the apparatus cancomprise a Josephson junction located at the position, which cancomprise an insulating barrier that can connect the first pattern ofsuperconductor material and the second pattern of superconductormaterial. An advantage of such an apparatus can be a gradiometric SQUIDstructure that can be sensitive to spatial variations in magneticfields.

In some examples of the apparatus, the first pattern of superconductingmaterial can be operably coupled to a first capacitor pad, and thesecond pattern of superconducting material can extend across the firstpattern of superconducting material to operably couple to a secondcapacitor pad. An advantage of such an apparatus can be theimplementation of a dipole gradiometric SQUID.

According to an embodiment, an apparatus is provided. The apparatus cancomprise a ring of superconductor material. The apparatus can alsocomprise a path of superconductor material positioned across the ring ofsuperconductor material. Additionally, the apparatus can comprise aJosephson junction, which can comprise an insulating barrier that canconnect the ring of superconductor material and the path ofsuperconductor material. An advantage of such an apparatus can be agradiometric SQUID structure that is suitable for quantum qubits.

In some examples of the apparatus, the Josephson junction can be locatedat a position where the path of superconducting material crosses overthe ring of superconducting material. An advantage of such an apparatus,can be alleviation of the need to separate crossing patterns ofsuperconducting material with a dielectric spacer.

According to an embodiment, an apparatus is provided. The apparatus cancomprise a first superconducting pathway located on a substrate. Theapparatus can also comprise a second superconducting pathway that cancross over the first superconducting pathway at a position. Theapparatus can further comprise a Josephson junction located at theposition. The Josephson junction can comprise a first superconductormaterial of the first superconducting pathway, a second superconductormaterial of the second superconducting pathway, and an insulatingbarrier. An advantage of such an apparatus can be a parallelgradiometric SQUID structure that can be more compact than conventionalgradiometric SQUID designs.

In some examples, the apparatus can also comprise a thirdsuperconducting pathway. The third superconducting pathway can crossover the first superconducting pathway at a second position. Further,the apparatus can comprise a second Josephson junction located at thesecond position. The second Josephson junction can comprise the firstsuperconductor material, a third superconductor material of the thirdsuperconducting pathway, and a second insulating barrier. An advantageof such an apparatus can be one or more parallel gradiometric SQUIDimplementations having four or more magnetic poles.

According to an embodiment, a method is provided. The method cancomprise depositing a first superconducting material onto a substrate.The method can also comprise forming an insulating barrier on a surfaceof the first superconducting material that is opposite to the substrate.Further, the method can comprise depositing a second superconductingmaterial over the insulating barrier to form a Josephson junction. Anadvantage of such a method can be that the method can enable the use ofelectron beam lithography and/or optical lithography in themanufacturing of one or more gradiometric SQUIDs.

In some examples of the method, forming the insulating barrier cancomprise oxidizing the first superconductor material. An advantage ofsuch a method can be that the method can enable the use ofsuperconductor-insulator-superconductor Josephson junctions tofacilitate a crossover of superconducting material in a gradiometricSQUID that is suitable for quantum qubits.

According to an embodiment, a method is provided. The method cancomprise forming a first pattern of superconducting material on asubstrate. The method can also comprise forming an insulating barrieradjacent to the first pattern of superconducting material such that thefirst pattern of superconducting material separates the insulatingbarrier from the substrate. Further, the method can comprise forming asecond pattern of superconducting material across the insulating barrierto form a Josephson junction. An advantage of such a method is that sucha method can facilitate creation of a parallel gradiometric SQUID thatcan allow for frequency tuning using an external magnetic flux.

In some examples of the method, the forming the first superconductingmaterial can comprise evaporating the first superconductor material ontothe semiconductor substrate. Also, the forming the secondsuperconducting material can comprise evaporating the secondsuperconducting material over the insulating barrier. An advantage ofsuch a method can be that the method enables use of the Manhattan stylefabrication technique to streamline a manufacturing of one or moregradiometric SQUIDs that are suitable for quantum qubits.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 illustrates a diagram of an example, non-limiting dipolegradiometric superconducting quantum interface device in accordance withone or more embodiments described herein.

FIG. 2 illustrates a diagram of an example, non-limiting quadrupole polegradiometric superconducting quantum interface device in accordance withone or more embodiments described herein.

FIG. 3 illustrates a diagram of an example, non-limiting multipolegradiometric superconducting quantum interface device in accordance withone or more embodiments described herein.

FIG. 4A illustrates a diagram of an example, non-limiting dipoleimplementation of a gradiometric superconducting quantum interfacedevice during a first stage of manufacturing in accordance with one ormore embodiments described herein.

FIG. 4B illustrates a diagram of an example, non-limiting quadrupolepole implementation of a gradiometric superconducting quantum interfacedevice during a first stage of manufacturing in accordance with one ormore embodiments described herein.

FIG. 4C illustrates a diagram of an example, non-limiting multipoleimplementation of a gradiometric superconducting quantum interfacedevice during a first stage of manufacturing in accordance with one ormore embodiments described herein.

FIG. 5A illustrates a diagram of an example, non-limiting dipoleimplementation of a gradiometric superconducting quantum interfacedevice during a second stage of manufacturing in accordance with one ormore embodiments described herein.

FIG. 5B illustrates a diagram of an example, non-limiting quadrupolepole implementation of a gradiometric superconducting quantum interfacedevice during a second stage of manufacturing in accordance with one ormore embodiments described herein.

FIG. 5C illustrates a diagram of an example, non-limiting multipoleimplementation of a gradiometric superconducting quantum interfacedevice during a second stage of manufacturing in accordance with one ormore embodiments described herein.

FIG. 6A illustrates a diagram of an example, non-limiting dipoleimplementation of a gradiometric superconducting quantum interfacedevice during a third stage of manufacturing in accordance with one ormore embodiments described herein.

FIG. 6B illustrates a diagram of an example, non-limiting quadrupolepole implementation of a gradiometric superconducting quantum interfacedevice during a third stage of manufacturing in accordance with one ormore embodiments described herein.

FIG. 6C illustrates a diagram of an example, non-limiting multipoleimplementation of a gradiometric superconducting quantum interfacedevice during a third stage of manufacturing in accordance with one ormore embodiments described herein.

FIG. 7A illustrates a diagram of an example, non-limiting dipoleimplementation of a gradiometric superconducting quantum interfacedevice during a fourth stage of manufacturing in accordance with one ormore embodiments described herein.

FIG. 7B illustrates a diagram of an example, non-limiting quadrupolepole implementation of a gradiometric superconducting quantum interfacedevice during a fourth stage of manufacturing in accordance with one ormore embodiments described herein.

FIG. 7C illustrates a diagram of an example, non-limiting multipoleimplementation of a gradiometric superconducting quantum interfacedevice during a fourth stage of manufacturing in accordance with one ormore embodiments described herein.

FIG. 8 illustrates a flow diagram of an example, non-limiting methodthat can facilitate manufacturing of one or more gradiometricsuperconducting quantum interface devices in accordance with one or moreembodiments described herein.

FIG. 9 illustrates a flow diagram of an example, non-limiting methodthat can facilitate manufacturing of one or more gradiometricsuperconducting quantum interface devices in accordance with one or moreembodiments described herein.

FIG. 10 illustrates a flow diagram of an example, non-limiting methodthat can facilitate manufacturing of one or more gradiometricsuperconducting quantum interface devices in accordance with one or moreembodiments described herein.

DETAILED DESCRIPTION

The following detailed description is merely illustrative and is notintended to limit embodiments and/or application or uses of embodiments.Furthermore, there is no intention to be bound by any expressed orimplied information presented in the preceding Background or Summarysections, or in the Detailed Description section.

One or more embodiments are now described with reference to thedrawings, wherein like referenced numerals are used to refer to likeelements throughout. In the following description, for purposes ofexplanation, numerous specific details are set forth in order to providea more thorough understanding of the one or more embodiments. It isevident, however, in various cases, that the one or more embodiments canbe practiced without these specific details.

Given the above problems with conventional gradiometric SQUIDs, thepresent disclosure can be implemented to produce a solution to one ormore of these problems in the form of one or more gradiometric parallelSQUIDs without conventional crossover locations that comprise adielectric spacer. Advantageously, the one or more gradiometric parallelSQUIDs described herein do not require the positioning of dielectricmaterial that is common to conventional gradiometric SQUIDs, do notcreate isolated segments of superconducting material (e.g., islands ofsuperconducting material), and/or can be suitable for superconductingquantum bits. Further, the one or more gradiometric parallel SQUIDsincluded in the various embodiments herein can be less sensitive toabsolute magnetic flux variations than conventional gradiometric SQUIDsand therefore can be less prone to dephasing due to bias flux noiseand/or charge noise than conventional gradiometric implementations.Additionally, the various embodiments of the one or more gradiometricSQUIDs described herein can allow for frequency tuning using one or moreexternal magnetic fluxes.

Various embodiments described herein can regard one or more gradiometricparallel SQUIDs comprising one or more Josephson junctions and that donot require conventional crossover locations nor introduce islands ofsuperconducting material. The one or more gradiometric parallel SQUIDsdescribed herein can be well suited for implementation using doubleangle evaporation, that can be used for superconducting qubits. Further,in one or more embodiments the gradiometric parallel SQUIDs can becharacterized by a compact design that can be implemented using electronbeam lithography and/or optical lithography. Additionally, variousembodiments described herein can regard one or more methods ofmanufacturing the one or more gradiometric parallel SQUIDs. For example,in one or more embodiments a thin insulating barrier can be constructedon a top surface of a loop of superconducting material; whereupon apattern of a second superconducting material can be deposited across theloop, thereby enabling for one or more Josephson junctions between thetwo superconducting materials. The one or more gradiometric parallelSQUIDs can comprise two or more loops of superconducting material,wherein circulating current through the one or more Josephson junctionscan depend on a difference in magnetic field in the two loops. Thus, thevarious gradiometric parallel SQUIDs described herein can be sensitiveto spatial variations in magnetic fields rather than magnetic fieldmagnitudes (e.g., which is common to conventional gradiometric SQUIDs).

FIG. 1 illustrates a diagram of an example, non-limiting top-down viewof a gradiometric SQUID 100 that can comprise one or more Josephsonjunctions 102 in accordance with one or more embodiments describedherein. As shown in FIG. 1, the gradiometric SQUID 100 can be a parallelSQUID comprising one or more first superconducting materials 104 locatedon one or more substrates 106 and operably coupled to one or more firstcapacitor pads 108. Additionally, the gradiometric SQUID 100 cancomprise one or more second superconducting materials 110 located on theone or more substrates 106 and operably coupled to one or more secondcapacitor pads 112.

The one or more substrates 106 can be, for example, one or moresemiconductor substrates. The one or more substrates 106 can support oneor more features of the one or more gradiometric SQUIDs 100. Examplematerials that can comprise the one or more substrates 106 can include,but are not limited to: silicon, germanium, silicon carbide, carbondoped silicon, compound semiconductors (e.g., comprising elements fromperiodic table groups III, IV, and/or V), silicon oxide, a combinationthereof, and/or the like. For instance, the one or more substrates 106can be a bulk silicon wafer and/or a silicon-on-insulator (“SOT”) wafer.Additionally, the one or more substrates 106 can comprise electronicstructures such as isolation wires (not shown). Further, the one or moresubstrates 106 can be characterized by one or more crystallinestructures. For example, the one or more substrates 106 can comprisesilicon <100>, silicon <110>, and/or silicon <111>, as described usingMiller indices. One of ordinary skill in the art will readily recognizethat the thickness of the one or more substrates 106 can vary dependingon: the composition of the one or more substrates 106, the desiredfunction of the gradiometric SQUID 100, a combination thereof, and/orthe like.

The one or more first superconducting materials 104 can be positioned onthe one or more substrates 106 in one or more first patterns. Forexample, the one or more first superconducting materials 104 can bearranged in a ring formation (e.g., as shown in FIG. 1), wherein thering can have a circular shape, a polygonal shape (e.g., as shown inFIG. 1), and/or an irregular shape. Example materials that can comprisethe one or more first superconducting materials 104 can include, but arenot limited to: aluminum, niobium, titanium, rhenium, indium, tungsten,titanium niobite, niobium titanium niobate, type-1 superconductingmaterials, type-2 superconducting materials, alloys thereof, compositesthereof, combinations thereof, and/or the like. The one or more firstpatterns of the one or more first superconducting materials 104 cancomprise a uniform distribution of the one or more first superconductingmaterials 104. Alternatively, the one or more first patterns of the oneor more first superconducting materials 104 can comprise a non-uniformdistribution of the one or more first superconducting materials 104. Forexample, the one or more first superconducting materials 104 cancomprise a first superconducting metal located at one portion of thefirst pattern and a second superconducting metal located at anotherportion of the first pattern. Thus, the first pattern of the one or morefirst superconducting materials 104 can be electrically continuous witha varying composition of the one or more first superconducting materials104 at different portions of the first pattern.

One of ordinary skill in the art will recognize that a thickness (e.g.,a height of extension from the one or more substrates 106) of the one ormore first superconducting materials 104 can vary depending on thecomposition of the one or more first superconducting materials 104and/or functionality of the one or more gradiometric SQUIDs 100. Forinstance, the thickness of the one or more first superconductingmaterials 104 can be exemplary greater than or equal to 0.5 microns andless than or equal to 1000 microns. Similarly, a width (e.g., along the“Y” axis where the one or more first superconducting materials 104 meetthe one or more first capacitor pads 108 in the example implementationpresented in FIG. 1) of the one or more first superconducting materials104 can vary depending on the composition of the one or more firstsuperconducting materials 104 and/or functionality of the one or moregradiometric SQUIDs 100. For instance, the width of the one or morefirst superconducting materials 104 can be exemplary greater than orequal to 0.5 microns and less than or equal to 1000 microns. The one ormore first superconducting materials 104 can be operably (e.g.,electrically) coupled to one or more first capacitor pads 108.

Each of the one or more first capacitor pads 108 can correlate to arespective magnetic pole of the gradiometric SQUID 100. The one or morefirst capacitor pads 108 can be connected to the one or more firstsuperconducting materials 104 and/or can oscillate at a frequency of thesubject qubit facilitated by the gradiometric SQUID 100. While FIG. 1depicts the one or more first capacitor pads 108 having a rectangularshape, the architecture of the one or more first capacitor pads 108 isnot so limited. One of ordinary skill in the art will recognize that theone or more first capacitor pads 108 can have a variety of shapesdependent of the functionality of the gradiometric SQUID 100. Examplematerials that can comprise the one or more first capacitor pads 108 caninclude, but are not limited to: aluminum, niobium, titanium, rhenium,indium, tungsten, titanium niobite, niobium titanium niobate, acombination thereof, and/or the like.

The one or more second superconducting materials 110 can be positionedon the one or more substrates 106 in one or more second patterns. Forexample, the one or more second superconducting materials 110 can bearranged in a path formation (e.g., as shown in FIG. 1), wherein thepath can extend straight (e.g., as shown in FIG. 1), can comprise bends,and/or can comprise curves. Example materials that can comprise the oneor more second superconducting materials 110 can include, but are notlimited to: aluminum, niobium, titanium, rhenium, indium, tungsten,titanium niobite, niobium titanium niobite, type-1 superconductingmaterials, type-2 superconducting materials, alloys thereof, compositesthereof, combinations thereof, and/or the like. In one or moreembodiments, the one or more second superconducting materials 110 cancomprise the same materials and/or can be characterized by the same orsubstantially same composition as the one or more first superconductingmaterials 104. Alternatively, in one or more embodiments, the one ormore second superconducting materials 110 can comprise differentmaterials and/or can be characterized by a different composition as theone or more first superconducting materials 104.

Further, the one or more second patterns of the one or more secondsuperconducting materials 110 can comprise a uniform distribution of theone or more second superconducting materials 110. Alternatively, the oneor more second patterns of the one or more second superconductingmaterials 110 can comprise a non-uniform distribution of the one or moresecond superconducting materials 110. For example, the one or moresecond superconducting materials 110 can comprise a firstsuperconducting metal located at one portion of the second pattern and asecond superconducting metal located at another portion of the secondpattern. Thus, the second pattern of the one or more secondsuperconducting materials 110 can be electrically continuous with avarying composition of the one or more second superconducting materials110 at different portions of the second pattern.

One of ordinary skill in the art will recognize that a thickness (e.g.,a height of extension from the one or more substrates 106) of the one ormore second superconducting materials 110 can vary depending on thecomposition of the one or more second superconducting materials 110and/or functionality of the one or more gradiometric SQUIDs 100. Forinstance, the thickness of the one or more second conducting materials110 can be exemplary greater than or equal to 0.5 microns and less thanor equal to 1000 microns. Similarly, a width (e.g., along the “Y” axiswhere the one or more second conducting materials 110 meet the one ormore second capacitor pads 112 in the example implementation presentedin FIG. 1) of the one or more second superconducting materials 110 canvary depending on the composition of the one or more secondsuperconducting materials 110 and/or functionality of the one or moregradiometric SQUIDs 100. For instance, the width of the one or moresecond conducting materials 110 can be exemplary greater than or equalto 0.5 microns and less than or equal to 1000 microns. The one or moresecond superconducting materials 110 can be operably (e.g.,electrically) coupled to one or more second capacitor pads 112.

Each of the one or more second capacitor pads 108 can correlate to arespective magnetic pole of the gradiometric SQUID 100. Thus, thegradiometric SQUID 100 depicted in FIG. 1 can be a dipole implementationof the various features of the gradiometric SQUID 100 described herein.The one or more second capacitor pads 112 can be connected to the one ormore second superconducting materials 110 and/or can oscillate at afrequency of the subject qubit facilitated by the gradiometric SQUID100. While FIG. 1 depicts the one or more second capacitor pads 112having a rectangular shape, the architecture of the one or more secondcapacitor pads 112 is not so limited. One of ordinary skill in the artwill recognize that the one or more second capacitor pads 112 can have avariety of shapes dependent of the functionality of the gradiometricSQUID 100. Example materials that can comprise the one or more secondcapacitor pads 112 can include, but are not limited to: titanium,rhenium, indium, tungsten, titanium niobite, niobium titanium niobate, acombination thereof, and/or the like.

One or more Josephson junctions 102 can be located at one or morepositions where the one or more first superconducting materials 104 andthe one or more second superconducting materials 110 overlap. In otherwords, one or more Josephson junctions 102 can be located at one or morepositions where the one or more second patterns (e.g., paths of secondsuperconducting material 110) extend over the one or more first patterns(e.g., rings of first superconducting material 104). As shown in FIG. 1,the one or more Josephson junctions 102 can be depicted by a dash lined“X” FIG. 1. In one or more embodiments, the one or more Josephsonjunctions 102 can be superconductor-insulator-superconductor (“SIS”)Josephson junctions 102. For example, the one or more Josephsonjunctions 102 can comprise a thin insulating barrier between the one ormore first superconducting materials 104 and the one or more secondsuperconducting materials 110. The thin insulating barrier can weaklyconnect the one or more first superconducting materials 104 and the oneor more second superconducting materials 110 to facilitate tunneling inaccordance with the Josephson effect. Further, the one or more Josephsonjunctions 102 can be bicrystal grain-boundary junctions or biepitaxialgran-boundary junctions, step-edge junctions, via junctions, crystaljunctions, and/or the like.

In one or more embodiments, the one or more Josephson junctions 102 canconnect the one or more first patterns (e.g., rings) of the one or morefirst superconducting materials 104 and the one or more second patterns(e.g., paths) of the one or more second superconducting materials 110 tocreate a plurality of loops that can facilitate a plurality of magneticfluxes (e.g., a first magnetic flux depicted by “ϕ_(ext1)” in FIG. 1and/or a second magnetic flux depicted by “Φ_(ext2)”). For example, afirst portion of the one or more first superconducting materials 104 cancomprise a first layer of a respective Josephson junction 102, a secondportion of the one or more second superconducting materials 110 cancomprise a second layer of the respective Josephson junction 102, and/ora thin insulating barrier located between the first portion and thesecond portion can comprise a third layer the respective Josephsonjunction 102. As shown in FIG. 1, the second pattern (e.g., comprisingthe one or more second superconducting materials 110) can extend fromthe one or more second capacitor pad 112 across the first pattern (e.g.,comprising the one or more first superconducting materials 104).Additionally, a Josephson junction 102 can be located at one or morepositions where the first pattern and second pattern overlap (e.g.,where the one or more second superconducting materials 110 cross overthe one or more first superconducting materials 104). In one or moreembodiments, each pattern of superconducting material (e.g., the firstpattern of the one or more first superconducting material 104 and/or thesecond pattern of the one or more second superconducting material 110)can extend across each other to operably connect to a respectivecapacitor pad (e.g., a respective first capacitor pad 108 and/or arespective second capacitor pad 112). While a dipole gradiometric SQUID100 is depicted in FIG. 1, the architecture of the one or moregradiometric SQUIEDS is not so limited.

FIG. 2 illustrates a diagram of an example, non-limiting top-down viewof a gradiometric SQUID 100 having a quadrupole pole implementation inaccordance with one or more embodiments described herein. Repetitivedescription of like elements employed in other embodiments describedherein is omitted for sake of brevity. As shown in FIG. 2, the one ormore gradiometric SQUIDs 100 can comprise a plurality of first capacitorpads 108 and/or a plurality of second capacitor pads 112. For example,the gradiometric SQUID 100 can comprise two first capacitor pads 108and/or two second capacitor pads 112 for a total of four capacitor padsand/or four respective magnetic poles. For instance, the first pattern(e.g., a ring) of the one or more first superconducting materials 104can be operably (e.g., electrically) connected to two respective firstcapacitor pads 108 (e.g., as shown in FIG. 2). Likewise, the secondpattern (e.g., a path) of the one or more second superconductingmaterials 110 can be operably (e.g., electrically) connected to tworespective second capacitor pads 112.

While FIGS. 1 and 2 depict one or more gradiometric SQUIDs 100 that canfacilitate two magnetic fluxes, the architecture of the one or moregradiometric SQUIDs 100 is not so limited. Likewise, while FIGS. 1 and 2depict one or more gradiometric SQUIDs 100 that comprise two patterns ofsuperconducting materials (e.g., the first pattern of one or more firstsuperconducting materials 104 and/or the second pattern of one or moresecond superconducting materials 110), the architecture of the one ormore gradiometric SQUIDs 100 is not so limited.

FIG. 3 illustrates a diagram of an example, non-limiting top-down viewof a gradiometric SQUID 100 having a multipole pole implementation inaccordance with one or more embodiments described herein. Repetitivedescription of like elements employed in other embodiments describedherein is omitted for sake of brevity. As shown in FIG. 3, the one ormore gradiometric SQUIDs 100 can comprise three or more patterns ofsuperconducting material to facilitate four or more magnetic fluxes.

For example, the one or more first superconducting materials 104 (e.g.,patterned in a circular ring shape in the exemplary embodiment of FIG.3) can be operably connected to a plurality of first capacitor pads 108(e.g., connected to four first capacitor pads 108 in the exemplaryembodiment of FIG. 3), wherein each respective first capacitor pad 108can correlate to a respective magnetic pole. Additionally, the one ormore second superconducting materials 110 (e.g., patterned in a straightpath in the exemplary embodiment of FIG. 3) can be operably connected toa plurality of second capacitor pads 112 (e.g., connected to two secondcapacitor pads 112 in the exemplary embodiment of FIG. 3), wherein eachrespective second capacitor pad 112 can correlate to a respectivemagnetic pole. Moreover, the one or more gradiometric SQUIDs 100 cancomprise one or more additional superconducting materials, such as oneor more third superconducting materials 302.

For instance, the one or more third superconducting materials 302 can bepositioned on the one or more substrates 106 in one or more thirdpatterns. For example, the one or more third superconducting materials302 can be arranged in a path formation (e.g., as shown in FIG. 3),wherein the path can extend straight (e.g., as shown in FIG. 3), cancomprise bends, and/or can comprise curves. Example materials that cancomprise the one or more third superconducting materials 302 caninclude, but are not limited to: aluminum, niobium, titanium, rhenium,indium, tungsten, titanium niobite, niobium titanium niobate, alloysthereof, composites thereof, combinations thereof, and/or the like. Inone or more embodiments, the one or more third superconducting materials302 can comprise the same materials and/or can be characterized by thesame or substantially same composition as the one or more firstsuperconducting materials 104 and/or the one or more secondsuperconducting materials 110. Alternatively, in one or moreembodiments, the one or more third superconducting materials 302 cancomprise different materials and/or can be characterized by a differentcomposition as the one or more first superconducting materials 104and/or the one or more second superconducting materials 110.

Further, the one or more third patterns of the one or more thirdsuperconducting materials 302 can comprise a uniform distribution of theone or more third superconducting materials 302. Alternatively, the oneor more third patterns of the one or more third superconductingmaterials 302 can comprise a non-uniform distribution of the one or morethird superconducting materials 302. For example, the one or more thirdsuperconducting materials 302 can comprise a first superconducting metallocated at one portion of the third pattern and a second superconductingmetal located at another portion of the third pattern. Thus, the thirdpattern of the one or more third superconducting materials 302 can beelectrically continuous with a varying composition of the one or morethird superconducting materials 302 at different portions of the thirdpattern.

One of ordinary skill in the art will recognize that a thickness (e.g.,a height of extension from the one or more substrates 106) of the one ormore third superconducting materials 302 can vary depending on thecomposition of the one or more third superconducting materials 302and/or functionality of the one or more gradiometric SQUIDs 100. Forinstance, the thickness of the one or more third superconductingmaterials 302 can be exemplary greater than or equal to 0.5 microns andless than or equal to 1000 microns. Similarly, a width (e.g., along the“Y” axis where the one or more third superconducting materials 302 meetthe one or more third capacitor pads 304 in the example implementationpresented in FIG. 3) of the one or more third superconducting materials302 can vary depending on the composition of the one or more thirdsuperconducting materials 302 and/or functionality of the one or moregradiometric SQUIDs 100. For instance, the width of the one or morethird superconducting materials 302 can be exemplary greater than orequal to 0.5 microns and less than or equal to 1000 microns. The one ormore third superconducting materials 302 can be operably (e.g.,electrically) coupled to one or more third capacitor pads 304.

Each of the one or more third capacitor pads 304 can correlate torespective magnetic pole of the gradiometric SQUID 100. Thus, thegradiometric SQUID 100 depicted in FIG. 3 can be a multipoleimplementation of the various features of the gradiometric SQUID 100described herein. The one or more third capacitor pads 304 can beconnected to the one or more third superconducting materials 302 and/orcan oscillate at a frequency of the subject qubit facilitated by thegradiometric SQUID 100. While FIG. 3 depicts the one or more thirdcapacitor pads 304 having a rectangular shape, the architecture of theone or more third capacitor pads 304 is not so limited. One of ordinaryskill in the art will recognize that the one or more third capacitorpads 304 can have a variety of shapes dependent of the functionality ofthe gradiometric SQUID 100. Example materials that can comprise the oneor more third capacitor pads 304 can include, but are not limited to:aluminum, niobium, titanium, rhenium, indium, tungsten, titaniumniobite, niobium titanium niobate, a combination thereof, and/or thelike.

As shown in FIG. 3, one or more Josephson junctions 102 can be locatedwhere one pattern of superconducting material overlaps and/or otherwisecross over another pattern of superconducting material. For example, oneor more Josephson junctions 102 can be located where the first patternof the one or more first superconducting materials 104 cross the thirdpattern of the one or more third superconducting materials 302. Forinstance, one or more Josephson junctions 102 can connect the firstpattern of one or more first superconducting materials 104 and the thirdpattern of one or more third superconducting materials 302 just as oneor more Josephson junctions 102 can connect the first pattern of one ormore first superconducting materials 104 and the second pattern of oneor more second superconducting materials 110, as described herein. Thus,the third pattern of one or more third superconducting materials 302,along with one or more Josephson junctions 102 connected to the thirdpattern, can create one or more loops of superconducting material withinthe gradiometric SQUID 100, which can facilitate the occurrence ofadditional magnetic fluxes (e.g., the occurrence of four magnetic fluxesin the exemplary embodiment of FIG. 3, wherein the magnetic fluxes arerespectively depicted by ““Φ_(ext1)”, “Φ_(ext2)”, ““Φ_(ext3)”,“Φ_(ext4)”).

As shown in FIG. 3, the respective patterns of superconducting materialcan overlap each other, cross each other, and/or weave between eachother. Additionally, the respective patterns of superconducting materialcan extend from and/or extend between respective capacitor pads.

FIG. 4A illustrates a diagram of an example, non-limiting gradiometricSQUID 100 during a first stage of manufacturing in accordance with oneor more embodiments described herein. Repetitive description of likeelements employed in other embodiments described herein is omitted forsake of brevity. For example, FIG. 4A can depict the first stage ofmanufacturing of the exemplary embodiment of FIG. 1.

During a first stage of manufacturing, a first portion of the one ormore first superconducting materials 104 can be deposited onto the oneor more substrates 106. Depositing the first portion of the one or morefirst superconducting materials 104 during the first stage ofmanufacturing can partially form the first pattern (e.g., can partiallyform a ring pattern). Additionally, depositing the first portion of theone or more first superconducting materials 104 during the first stageof manufacturing can operably couple the one or more firstsuperconducting materials 104 to the one or more first capacitor pads108. As shown in FIG. 4A, during the first stage of manufacturing thefirst portion of the one or more first superconducting materials 104 canbe deposited onto the one or more substrates 106 at the desired locationof the first pattern except at the desired locations of the one or moreJosephson junctions 102. For example, a gap in the first pattern of oneor more first superconducting materials 104 can be created where the oneor more Josephson junctions 102 can be located.

Deposition of the first portion of the one or more first superconductingmaterials 104 during the first stage of manufacturing can be facilitateby one or more deposition techniques, which can include, but are notlimited to: thermal evaporation, electron beam evaporation, electronbeam sputtering, ion-sputtering, plasma sputtering, pulsed-lasersputtering, molecular-beam epitaxy (“MBE”) growth, epitaxial growth, acombination thereof, and/or the like. One of ordinary skill in the artwill recognize that the type of deposition technique utilized can varydepending on the composition of the first portion of the one or morefirst superconducting materials 104 and/or the design of the firstpattern. Additionally, the deposition can be facilitated by one or morelithography process, which can include, but are not limited to: electronbeam lithography, optical lithography, deep-ultraviolet lithography,direct laser lithography, a combination thereof, and/or the like.

FIG. 4B illustrates another diagram of an example, non-limitinggradiometric SQUID 100 during a first stage of manufacturing inaccordance with one or more embodiments described herein. Repetitivedescription of like elements employed in other embodiments describedherein is omitted for sake of brevity. For example, FIG. 4B can depictthe first stage of manufacturing of the exemplary embodiment of FIG. 2.The features of the first stage of manufacturing described herein withregards to FIG. 4A can also be implemented in the first stage ofmanufacturing in any of the various embodiments of the one or moregradiometric SQUIDs 100, such as the first stage of manufacturingdepicted in FIG. 4B.

FIG. 4C illustrates a further diagram of an example, non-limitinggradiometric SQUID 100 during a first stage of manufacturing inaccordance with one or more embodiments described herein. Repetitivedescription of like elements employed in other embodiments describedherein is omitted for sake of brevity. For example, FIG. 4C can depictthe first stage of manufacturing of the exemplary embodiment of FIG. 3.The features of the first stage of manufacturing described herein withregards to FIG. 4A can also be implemented in the first stage ofmanufacturing in any of the various embodiments of the one or moregradiometric SQUIDs 100, such as the first stage of manufacturingdepicted in FIG. 4C.

Additionally, as disclosed in FIG. 4C, a first portion of the one ormore second superconducting materials 110 can be deposited during thefirst stage of manufacturing to partially define the second pattern. Forexample, the first portion of the one or more first superconductingmaterials 104 can have the same composition as the first portion of theone or more second superconducting materials 110; thereby facilitating acommon deposition during the fourth stage of manufacturing. Therefore,at least a portion of the second pattern (e.g., comprising the one ormore second superconducting materials 110) can be deposited along withthe first portion of the one or more first superconducting materials104.

FIG. 5A illustrates a diagram of an example, non-limiting gradiometricSQUID 100 during a second stage of manufacturing in accordance with oneor more embodiments described herein. Repetitive description of likeelements employed in other embodiments described herein is omitted forsake of brevity. For example, FIG. 5A can depict the second stage ofmanufacturing of the exemplary embodiment of FIG. 1.

During a second stage of manufacturing, a second portion of the one ormore first superconducting materials 104 can be deposited onto the oneor more substrates 106. Depositing the second portion of the one or morefirst superconducting materials 104 during the second stage ofmanufacturing can complete the first pattern (e.g., a ring pattern). Asshown in FIG. 5A, the location of the deposition of the second portionof the one or more first superconducting materials 104 can be indicatedby a dash lined box. The second portion of the one or more firstsuperconducting materials 104 can be deposited at respective locationswhere there can be respective Josephson junctions 102 connecting the oneor more first superconducting materials 104 to one or more otherpatterns of superconducting materials (e.g., the second pattern of theone or more second superconducting materials 110). Additionally, thecomposition of the second portion of the one or more firstsuperconducting materials 104 can be the same or different than thecomposition of the first portion of the one or more firstsuperconducting materials 104. In one or more embodiments, the secondportion of the first superconducting materials 104 can be asuperconducting metal that can be subject to oxidation, such asaluminum.

Deposition of the second portion of the one or more firstsuperconducting materials 104 during the second stage of manufacturingcan be facilitate by one or more deposition techniques, which caninclude, but are not limited to: thermal evaporation, electron beamevaporation, electron beam sputtering, ion-sputtering, plasmasputtering, pulsed-laser sputtering, MBE growth, epitaxial growth, acombination thereof, and/or the like. One of ordinary skill in the artwill recognize that the type of deposition technique utilized can varydepending on the composition of the second portion of the one or morefirst superconducting materials 104 and/or the design of the firstpattern. Additionally, the deposition can be facilitated by one or morelithography process, which can include, but are not limited to: electronbeam lithography, optical lithography, deep-ultraviolet lithography,direct laser lithography, a combination thereof, and/or the like.

FIG. 5B illustrates another diagram of an example, non-limitinggradiometric SQUID 100 during a second stage of manufacturing inaccordance with one or more embodiments described herein. Repetitivedescription of like elements employed in other embodiments describedherein is omitted for sake of brevity. For example, FIG. 5B can depictthe second stage of manufacturing of the exemplary embodiment of FIG. 2.The features of the second stage of manufacturing described herein withregards to FIG. 5A can also be implemented in the second stage ofmanufacturing in any of the various embodiments of the one or moregradiometric SQUIDs 100, such as the second stage of manufacturingdepicted in FIG. 5B.

FIG. 5C illustrates a further diagram of an example, non-limitinggradiometric SQUID 100 during a second stage of manufacturing inaccordance with one or more embodiments described herein. Repetitivedescription of like elements employed in other embodiments describedherein is omitted for sake of brevity. For example, FIG. 5C can depictthe second stage of manufacturing of the exemplary embodiment of FIG. 3.The features of the second stage of manufacturing described herein withregards to FIG. 5A can also be implemented in the second stage ofmanufacturing in any of the various embodiments of the one or moregradiometric SQUIDs 100, such as the second stage of manufacturingdepicted in FIG. 5C.

Additionally, FIG. 5C illustrates that during the second stage ofmanufacturing, one or more portions of other patterns of superconductingmaterial can also be deposited. Also, as depicted in FIG. 5C, a secondportion of the one or more first superconducting materials 104 (e.g.,defined by dashed lines in FIG. 5C) can be deposited during the secondstage of manufacturing to further define the first pattern. The patternportions deposited during the second stage of manufacturing can comprisethe same materials. For example, as shown in FIG. 5C, the one or morethird superconducting materials 302 can be deposited during the secondstage of manufacturing along with the second portion of the one or morefirst superconducting materials 104, wherein the second portion of theone or more first superconducting materials 104 and the one or morethird superconducting materials 302 can have the same composition. Forinstance, the one or more third superconducting materials 302 and/or theone or more first superconducting materials 104 comprising the secondportion of the first pattern can be a superconducting metal that can besubject to oxidation, such as aluminum.

FIG. 6A illustrates a diagram of an example, non-limiting gradiometricSQUID 100 during a third stage of manufacturing in accordance with oneor more embodiments described herein. Repetitive description of likeelements employed in other embodiments described herein is omitted forsake of brevity. For example, FIG. 6A can depict the second stage ofmanufacturing of the exemplary embodiment of FIG. 1.

During a third stage of manufacturing, one or more insulating materials602 can be formed. The one or more insulating materials 602 can serve asone or more thin insulating barriers comprised with the one or moreJosephson junctions 102. For example, the one or more insulatingmaterials 602 can be formed at the future locations of Josephsonjunctions 102.

In one or more embodiments, the one or more insulating materials 602 canbe formed by oxidizing the superconducting materials deposited duringthe second stage of manufacturing. For example, as shown in FIG. 6A, thesecond portion of the one or more first superconducting materials 104can be oxidized to form the one or more insulating materials 602. Forinstance, the second portion of the first superconducting materials 104can be aluminum, which can be oxidized during the third stage ofmanufacturing to form one or more insulating materials 602 of aluminumoxide.

In various embodiments, the one or more insulating materials 602 can beformed on a top surface (e.g., a surface facing away from the one ormore substrates 106) of a superconducting material, such as one or moresections of the first pattern of the one or more first superconductingmaterials 104. One of ordinary skill in the art will recognize that athickness (e.g., a height of extension from the top surface of asuperconducting material) of the one or more insulating materials 602can vary depending on the composition of the one or more insulatingmaterials 602 and/or functionality of the one or more gradiometricSQUIDs 100. For instance, the thickness of the one or more insulatingmaterials 602 can be exemplary greater than or equal to 0.5 microns andless than or equal to 1000 microns.

FIG. 6B illustrates another diagram of an example, non-limitinggradiometric SQUID 100 during a third stage of manufacturing inaccordance with one or more embodiments described herein. Repetitivedescription of like elements employed in other embodiments describedherein is omitted for sake of brevity. For example, FIG. 6B can depictthe third stage of manufacturing of the exemplary embodiment of FIG. 2.The features of the third stage of manufacturing described herein withregards to FIG. 6A can also be implemented in the third stage ofmanufacturing in any of the various embodiments of the one or moregradiometric SQUIDs 100, such as the third stage of manufacturingdepicted in FIG. 6B.

FIG. 6C illustrates a further diagram of an example, non-limitinggradiometric SQUID 100 during a third stage of manufacturing inaccordance with one or more embodiments described herein. Repetitivedescription of like elements employed in other embodiments describedherein is omitted for sake of brevity. For example, FIG. 6C can depictthe third stage of manufacturing of the exemplary embodiment of FIG. 3.The features of the third stage of manufacturing described herein withregards to FIG. 6A can also be implemented in the third stage ofmanufacturing in any of the various embodiments of the one or moregradiometric SQUIDs 100, such as the third stage of manufacturingdepicted in FIG. 6C.

Additionally, FIG. 6C illustrates that during the third stage ofmanufacturing, a portion of superconducting material can be isolated forformation of the one or more insulating materials 602. For example, thethird pattern of the one or more third superconducting materials 302 canhave a uniform or substantially uniform composition, wherein somesections of the one or more third superconducting materials 302 canfacilitate formation of the one or more insulating materials 602 (e.g.,be oxidized) while other sections can remain unmodified during the thirdstage of manufacturing. For instance, one or more masking layers can beused during the third stage of manufacturing to direct the formation ofthe one or more insulating materials 602. Alternatively, in variousembodiments the one or more insulating materials 602 can be formed onany suitable superconducting materials without directing formation toparticular locations (e.g., the entire third pattern can be subject tooxidation and thereby form an oxidized top layer to serve as the one ormore insulating materials 602).

FIG. 7A illustrates a diagram of an example, non-limiting gradiometricSQUID 100 during a fourth stage of manufacturing in accordance with oneor more embodiments described herein. Repetitive description of likeelements employed in other embodiments described herein is omitted forsake of brevity. For example, FIG. 7A can depict the fourth stage ofmanufacturing of the exemplary embodiment of FIG. 1.

A fourth stage of manufacturing can comprise depositing additionalsuperconducting material to: form one or more additional patterns ofsuperconducting material, complete one or more partially existingpatterns of superconducting material, and/or form one or more Josephsonjunctions 102. For example, as shown in FIG. 7A, during the fourth stageof manufacturing, the one or more second superconducting materials 110can be deposited onto the one or more insulating materials 602 and/orthe one or more substrates 106 such that the second pattern of one ormore second superconducting materials 110 can be formed. As shown inFIG. 7A, the deposition of superconducting material during the fourthstage of manufacturing can form the second pattern, which can extendform the one or more second capacitor pads 112 across the first pattern(e.g., comprising the one or more first superconducting materials 104)and the one or more insulating materials 602; thereby forming one ormore Josephson junctions 102 and/or two loops of superconductingmaterial.

Deposition of the additional superconducting material (e.g., the one ormore second superconducting materials 110) during the fourth stage ofmanufacturing can be facilitate by one or more deposition techniques,which can include, but are not limited to: thermal evaporation, electronbeam evaporation, electron beam sputtering, ion-sputtering, plasmasputtering, pulsed-laser sputtering, MBE growth, epitaxial growth, acombination thereof, and/or the like. One of ordinary skill in the artwill recognize that the type of deposition technique utilized can varydepending on the composition of the additional superconducting materials(e.g., the one or more second superconducting materials 110) and/or thedesign of the first pattern. Additionally, the deposition can befacilitated by one or more lithography process, which can include, butare not limited to: electron beam lithography, optical lithography,deep-ultraviolet lithography, direct laser lithography, a combinationthereof, and/or the like.

FIG. 7B illustrates another diagram of an example, non-limitinggradiometric SQUID 100 during a fourth stage of manufacturing inaccordance with one or more embodiments described herein. Repetitivedescription of like elements employed in other embodiments describedherein is omitted for sake of brevity. For example, FIG. 7B can depictthe fourth stage of manufacturing of the exemplary embodiment of FIG. 2.The features of the fourth stage of manufacturing described herein withregards to FIG. 7A can also be implemented in the fourth stage ofmanufacturing in any of the various embodiments of the one or moregradiometric SQUIDs 100, such as the fourth stage of manufacturingdepicted in FIG. 7B.

FIG. 7C illustrates a further diagram of an example, non-limitinggradiometric SQUID 100 during a fourth stage of manufacturing inaccordance with one or more embodiments described herein. Repetitivedescription of like elements employed in other embodiments describedherein is omitted for sake of brevity. For example, FIG. 7C can depictthe fourth stage of manufacturing of the exemplary embodiment of FIG. 3.The features of the fourth stage of manufacturing described herein withregards to FIG. 7A can also be implemented in the fourth stage ofmanufacturing in any of the various embodiments of the one or moregradiometric SQUIDs 100, such as the fourth stage of manufacturingdepicted in FIG. 7C.

Additionally, as shown in FIG. 7C, during the fourth stage ofmanufacturing a third portion (e.g., defined by dashed lines in FIG. 7C)of the first pattern of the one or more first superconducting materials104 can be deposited to complete the first pattern and/or form one ormore Josephson junctions 102. Further, a second portion of the one ormore second superconducting material 110 can be deposited to connect tothe previously deposited first portion of the one or more secondsuperconducting materials 110. The pattern portions deposited during thefourth stage of manufacturing can comprise the same materials. Forexample, the third portion of the one or more first superconductingmaterials 104 can have the same composition as the second portion of theone or more second superconducting materials 110; thereby facilitating acommon deposition during the fourth stage of manufacturing. Thus, thefourth stage of manufacturing can complete one or more partiallyestablished patterns of superconducting material, such as the firstpattern (e.g., comprising the one or more first superconductingmaterials 104) and/or the second pattern (e.g., comprising the one ormore second superconducting materials 110). Moreover, the depositionduring the fourth stage of manufacturing can create one or moreJosephson junctions 102 and/or a plurality of loops of superconductingmaterial.

Thus, the manufacturing stages described with regards to FIGS. 4A-7C canachieve multiple electrically continuous patterns of superconductingmaterials. For example, a first electrically continuous pattern of theone or more first superconducting materials 104 can be formed, a secondelectrically continuous pattern of the one or more secondsuperconducting materials 110 can be formed, and/or a third electricallycontinuous pattern of the one or more third superconducting materials302 can be formed. Additionally, the respective patterns can comprisenon-uniform distributions of superconducting materials. For example, thefirst electrically continuous pattern of the one or more firstsuperconducting materials 104 can comprise: a superconducting materialof the one or more first superconducting materials 104 at a firstportion of the first pattern, another superconducting material of theone or more superconducting materials 104 at a second portion of thefirst pattern, and/or still another superconducting material of the oneor more superconducting materials 104 at a third portion of the firstpattern. Moreover, one of ordinary skill in the art will recognize thatfurther patterns of superconducting materials in addition to the threeshown in FIGS. 4A-7C are also envisaged.

FIG. 8 illustrates a flow diagram of an example, non-limiting method 800that can facilitate manufacturing one or more gradiometric SQUIDs 100 inaccordance with one or more embodiments described herein. Repetitivedescription of like elements employed in other embodiments describedherein is omitted for sake of brevity.

At 802, the method 800 can comprise depositing one or more firstsuperconducting materials 104 onto one or more substrates 106 (e.g., asdescribed herein with regards to the first stage and/or second stage ofmanufacturing exemplarily depicted in FIGS. 4A-5C). The depositing at802 can be facilitate by one or more deposition techniques, which caninclude, but are not limited to: evaporation, thermal evaporation,electron beam evaporation, electron beam sputtering, ion-sputtering,plasma sputtering, pulsed-laser sputtering, MBE growth, epitaxialgrowth, a combination thereof, and/or the like. The depositing at 802can form one or more first patterns of the one or more firstsuperconducting materials 104. For example, the one or more firstpatterns can be ring formations as described in various embodimentsherein. Additionally, the depositing at 802 can facilitate operably(electrically) coupling the one or more first superconducting materials104 to one or more first capacitor pads 108. Further, the deposition canbe facilitated by one or more lithography process, which can include,but are not limited to: electron beam lithography, optical lithography,deep-ultraviolet lithography, direct laser lithography, a combinationthereof, and/or the like.

At 804, the method 800 can comprise forming one or more insulatingbarriers (e.g., one or more insulating materials 602) on a surface ofthe one or more first superconducting materials 104 that can be oppositeto the one or more substrates 106 (e.g., as described herein withregards to the third stage of manufacturing exemplarily depicted inFIGS. 6A-6C). For example, the surface can be a top surface of the oneor more first superconducting materials 104.

In one or more embodiments, the forming at 804 can comprise oxidizingone or more first conducting materials previously deposited (e.g., at802) onto the one or more substrates 106.

At 806, the method 800 can comprise depositing one or more secondsuperconducting materials 110 over the one or more insulating barriers(e.g., one or more insulating materials 602) to form one or moreJosephson junctions 102 (e.g., as described herein with regards to thefourth stage of manufacturing exemplarily depicted in FIGS. 7A-7C). Thedepositing at 806 can be facilitate by one or more depositiontechniques, which can include, but are not limited to: evaporation,thermal evaporation, electron beam evaporation, electron beamsputtering, ion-sputtering, plasma sputtering, pulsed-laser sputtering,MBE growth, epitaxial growth, a combination thereof, and/or the like.The depositing at 806 can form one or more second patterns of the one ormore second superconducting materials 110. Additionally, the depositioncan be facilitated by one or more lithography process, which caninclude, but are not limited to: electron beam lithography, opticallithography, deep-ultraviolet lithography, direct laser lithography, acombination thereof, and/or the like. For example, the one or moresecond patterns can be path formations as described in variousembodiments herein. Additionally, the depositing at 806 can facilitateoperably (electrically) coupling the one or more second superconductingmaterials 110 to one or more second capacitor pads 112. In one or moreembodiments, the depositing at 806 can further complete one or morepartially completed patterns of superconducting material located on theone or more substrates 106.

FIG. 9 illustrates a flow diagram of an example, non-limiting method 900that can facilitate manufacturing one or more gradiometric SQUIDs 100 inaccordance with one or more embodiments described herein. Repetitivedescription of like elements employed in other embodiments describedherein is omitted for sake of brevity.

At 902, the method 900 can comprise forming a first pattern (e.g., aring formation) of superconducting material (e.g., one or more firstsuperconducting materials 104) on one or more substrates 106 (e.g., asdescribed herein with regards to the first stage and/or second stage ofmanufacturing exemplarily depicted in FIGS. 4A-5C). The forming at 902can be facilitate by one or more deposition techniques, which caninclude, but are not limited to: evaporation, thermal evaporation,electron beam evaporation, electron beam sputtering, ion-sputtering,plasma sputtering, pulsed-laser sputtering, MBE growth, epitaxialgrowth, a combination thereof, and/or the like. Further, the depositioncan be facilitated by one or more lithography process, which caninclude, but are not limited to: electron beam lithography, opticallithography, deep-ultraviolet lithography, direct laser lithography, acombination thereof, and/or the like. Additionally, the forming at 902can facilitate operably (electrically) coupling the one or moresuperconducting materials (e.g., the one or more first superconductingmaterials 104) to one or more first capacitor pads 108. The firstpattern formed at 902 can be a complete pattern of superconductingmaterial or a partial pattern of superconducting material.

At 904, the method 900 can comprise forming one or more insulatingbarriers (e.g., one or more insulating materials 602) adjacent to thefirst pattern of the one or more superconducting materials (e.g., one ormore first superconducting materials 104) such that the first pattern ofsuperconducting material can separate the one or more insulatingbarriers (e.g., one or more insulating material 602) from the one ormore substrates 106 (e.g., as described herein with regards to the thirdstage of manufacturing exemplarily depicted in FIGS. 6A-6C). Forexample, the one or more insulating barriers can be formed on a topsurface of the one or more superconducting materials. In one or moreembodiments, the forming at 904 can comprise oxidizing one or moreportions of the one or more superconducting materials.

At 906, the method 900 can comprise forming one or more second patternsof superconducting material across the one or more insulating barriersto form one or more Josephson junctions 102 (e.g., as described hereinwith regards to the fourth stage of manufacturing exemplarily depictedin FIGS. 7A-7C). The forming at 906 can be facilitate by one or moredeposition techniques, which can include, but are not limited to:evaporation, thermal evaporation, electron beam evaporation, electronbeam sputtering, ion-sputtering, plasma sputtering, pulsed-lasersputtering, MBE growth, epitaxial growth, a combination thereof, and/orthe like. Further, the deposition can be facilitated by one or morelithography process, which can include, but are not limited to: electronbeam lithography, optical lithography, deep-ultraviolet lithography,direct laser lithography, a combination thereof, and/or the like.Additionally, the forming at 906 can facilitate operably (electrically)coupling the one or more superconducting materials (e.g., one or moresecond superconducting materials 110) to one or more second capacitorpads 112. In one or more embodiments, the forming at 906 can furthercomplete one or more partially completed patterns of superconductingmaterial located on the one or more substrates 106.

FIG. 10 illustrates a flow diagram of an example, non-limiting method1000 that can facilitate manufacturing one or more gradiometric SQUIDs100 in accordance with one or more embodiments described herein.Repetitive description of like elements employed in other embodimentsdescribed herein is omitted for sake of brevity.

At 1002, the method 1000 can comprise forming a first portion of a firstpattern (e.g., a ring formation) of superconducting material (e.g., oneor more first superconducting materials 104) on one or more substrates106 (e.g., as described herein with regards to the first stageexemplarily depicted in FIGS. 4A-4C). The forming at 1002 can befacilitate by one or more deposition techniques, which can include, butare not limited to: evaporation, thermal evaporation, electron beamevaporation, electron beam sputtering, ion-sputtering, plasmasputtering, pulsed-laser sputtering, MBE growth, epitaxial growth, acombination thereof, and/or the like. Further, the deposition can befacilitated by one or more lithography process, which can include, butare not limited to: electron beam lithography, optical lithography,deep-ultraviolet lithography, direct laser lithography, a combinationthereof, and/or the like. Additionally, the forming at 1002 canfacilitate operably (electrically) coupling the one or moresuperconducting materials (e.g., the one or more first superconductingmaterials 104) to one or more first capacitor pads 108.

At 1004, the method 1000 can comprise forming a second portion of thefirst pattern on the one or more substrates 106 and connected to thefirst portion of the first pattern (e.g., as described herein withregards to the first stage exemplarily depicted in FIGS. 5A-5C). Forexample, the superconducting material comprising the first portion ofthe first pattern can have a different composition than thesuperconducting material comprising the second portion of the firstpattern. The forming at 1004 can be facilitate by one or more depositiontechniques, which can include, but are not limited to: evaporation,thermal evaporation, electron beam evaporation, electron beamsputtering, ion-sputtering, plasma sputtering, pulsed-laser sputtering,MBE growth, epitaxial growth, a combination thereof, and/or the like.Additionally, the deposition can be facilitated by one or morelithography process, which can include, but are not limited to: electronbeam lithography, optical lithography, deep-ultraviolet lithography,direct laser lithography, a combination thereof, and/or the like.

At 1006, the method 1000 can comprise forming one or more insulatingbarriers (e.g., one or more insulating materials 602) adjacent to thesecond portion such that the first pattern of superconducting materialcan separate the one or more insulating barriers (e.g., one or moreinsulating material 602) from the one or more substrates 106 (e.g., asdescribed herein with regards to the third stage of manufacturingexemplarily depicted in FIGS. 6A-6C). For example, the one or moreinsulating barriers can be formed on a top surface of the one or moresuperconducting materials comprising the second portion of the firstpattern. In one or more embodiments, the forming at 1006 can compriseoxidizing the second portion of the first pattern of one or moresuperconducting materials.

At 1008, the method 1000 can comprise forming one or more secondpatterns of superconducting material across the one or more insulatingbarriers to form one or more Josephson junctions 102 (e.g., as describedherein with regards to the fourth stage of manufacturing exemplarilydepicted in FIGS. 7A-7C). The forming at 1006 can be facilitate by oneor more deposition techniques, which can include, but are not limitedto: evaporation, thermal evaporation, electron beam evaporation,electron beam sputtering, ion-sputtering, plasma sputtering,pulsed-laser sputtering, MBE growth, epitaxial growth, a combinationthereof, and/or the like. Further, the deposition can be facilitated byone or more lithography process, which can include, but are not limitedto: electron beam lithography, optical lithography, deep-ultravioletlithography, direct laser lithography, a combination thereof, and/or thelike. Additionally, the forming at 1006 can facilitate operably(electrically) coupling the one or more superconducting materials (e.g.,one or more second superconducting materials 110) to one or more secondcapacitor pads 112. In one or more embodiments, the forming at 1008 canfurther complete one or more partially completed patterns ofsuperconducting material located on the one or more substrates 106.

One of ordinary skill in the art will recognize that the variousfeatures and/or embodiments of the stages of manufacturing describedherein with regards to FIG. 4A-7C can facilitate the various featuresand/or embodiments of the methods described herein (e.g., method 800,method 900, and/or method 1000). Further, the various methods describedherein can facilitate manufacturing of any and/or all of the numerousembodiments described herein.

In addition, the term “or” is intended to mean an inclusive “or” ratherthan an exclusive “or.” That is, unless specified otherwise, or clearfrom context, “X employs A or B” is intended to mean any of the naturalinclusive permutations. That is, if X employs A; X employs B; or Xemploys both A and B, then “X employs A or B” is satisfied under any ofthe foregoing instances. Moreover, articles “a” and “an” as used in thesubject specification and annexed drawings should generally be construedto mean “one or more” unless specified otherwise or clear from contextto be directed to a singular form. As used herein, the terms “example”and/or “exemplary” are utilized to mean serving as an example, instance,or illustration. For the avoidance of doubt, the subject matterdisclosed herein is not limited by such examples. In addition, anyaspect or design described herein as an “example” and/or “exemplary” isnot necessarily to be construed as preferred or advantageous over otheraspects or designs, nor is it meant to preclude equivalent exemplarystructures and techniques known to those of ordinary skill in the art.

It is, of course, not possible to describe every conceivable combinationof components, products and/or methods for purposes of describing thisdisclosure, but one of ordinary skill in the art can recognize that manyfurther combinations and permutations of this disclosure are possible.Furthermore, to the extent that the terms “includes,” “has,”“possesses,” and the like are used in the detailed description, claims,appendices and drawings such terms are intended to be inclusive in amanner similar to the term “comprising” as “comprising” is interpretedwhen employed as a transitional word in a claim. The descriptions of thevarious embodiments have been presented for purposes of illustration,but are not intended to be exhaustive or limited to the embodimentsdisclosed. Many modifications and variations will be apparent to thoseof ordinary skill in the art without departing from the scope and spiritof the described embodiments. The terminology used herein was chosen tobest explain the principles of the embodiments, the practicalapplication or technical improvement over technologies found in themarketplace, or to enable others of ordinary skill in the art tounderstand the embodiments disclosed herein.

1. An apparatus, comprising: a first pattern of superconducting materiallocated on a substrate; a second pattern of superconducting materialthat extends across the first pattern of superconducting material at aposition; and a Josephson junction located at the position andcomprising an insulating barrier that connects the first pattern ofsuperconducting material and the second pattern of superconductingmaterial; a third pattern of superconducting material that extendsacross the first pattern of superconducting material at a secondposition; and a second Josephson junction located at the secondposition, wherein the second Josephson junction comprises a firstportion of the first pattern of superconducting material, a secondportion of third pattern of superconducting material, and a secondinsulating barrier.
 2. The apparatus of claim 1, wherein the firstpattern of superconducting material is operably coupled to a firstcapacitor pad, and wherein the second pattern of superconductingmaterial extends across the first pattern of superconducting material tooperably couple to a second capacitor pad.
 3. The apparatus of claim 1,wherein the apparatus is a gradiometric superconducting quantuminterference device.
 4. The apparatus of claim 3, wherein the Josephsonjunction is a superconductor-insulator-superconductor Josephson junctionthat comprises a first superconductor metal comprised within the firstpattern of superconducting material and a second superconductor metalcomprised within the second pattern of superconducting material.
 5. Theapparatus of claim 4, wherein the first superconductor metal is selectedfrom a first group consisting of a type-1 superconducting material and atype-2 superconducting material, wherein the second superconductor metalis selected from a second group consisting of the type-1 superconductingmaterial and the type-2 superconducting material, and wherein theinsulating barrier is an electrically insulating dielectric material atlow temperature.
 6. The apparatus of claim 4, wherein the secondJosephson junction is a second superconductor-insulator-superconductorJosephson junction.
 7. An apparatus, comprising: a ring ofsuperconductor material; a path of superconductor material positionedacross the ring of superconductor material; and a Josephson junctioncomprising an insulating barrier that connects the ring ofsuperconductor material and the path of superconductor material.
 8. Theapparatus of claim 7, wherein the Josephson junction is located at aposition where the path of superconductor material crosses over the ringof superconductor material.
 9. The apparatus of claim 8, wherein theapparatus is a gradiometric superconducting quantum interference device,and wherein the Josephson junction is asuperconductor-insulator-superconductor Josephson junction.
 10. Theapparatus of claim 9, wherein the ring of superconductor material andthe path of superconductor material are located on a semiconductorsubstrate, wherein the ring of superconductor material is operablycoupled to a first capacitor pad, and wherein the path of superconductormaterial crosses over the ring of superconductor material to operablyconnect to a second capacitor pad.
 11. The apparatus of claim 10,wherein the ring of superconductor material comprises a materialselected from a first group consisting of a type-1 superconductingmaterial and a type-2 superconducting material, wherein the path ofsuperconductor material comprises another material selected from asecond group consisting of the type-1 superconducting material and thetype-2 superconducting material, and wherein the insulating barrier isan electrically insulating dielectric material at low temperature. 12.An apparatus, comprising: a first superconducting pathway located on asubstrate; a second superconducting pathway that crosses over the firstsuperconducting pathway at a position; a Josephson junction located atthe position and comprising a first superconductor material of the firstsuperconducting pathway, a second superconductor material of the secondsuperconducting pathway, and an insulating barrier; a thirdsuperconducting pathway that crosses over the first superconductingpathway at a second position; and a second Josephson junction located atthe second position, wherein the second Josephson junction comprises afirst superconductor material of the first superconducting pathway, athird superconductor material of the third superconducting pathway, anda second insulating barrier.
 13. (canceled)
 14. The apparatus of claim14, wherein the apparatus is a gradiometric superconducting quantuminterference device, wherein the Josephson junction is a firstsuperconductor-insulator-superconductor Josephson junction, and whereinthe second Josephson junction is a secondsuperconductor-insulator-superconductor Josephson junction.
 15. Theapparatus of claim 14, wherein the first superconducting pathwaycomprises a first superconducting material selected from a first groupconsisting of a type-1 superconducting material and a type-2superconducting material, wherein the second superconducting pathwaycomprises a second superconducting material selected from a second groupconsisting of the type-1 superconducting material and the type-2superconducting material, wherein the third superconducting pathwaycomprises a third superconducting material selected from a third groupconsisting of the type-1 superconducting material and the type-2superconducting material, wherein the insulating barrier is anelectrically insulating dielectric material at low temperature.
 16. Amethod, comprising: depositing a first superconducting material onto asubstrate; forming an insulating barrier on a surface of the firstsuperconducting material that is opposite to the substrate; anddepositing a second superconducting material over the insulating barrierto form a Josephson junction at a position; and depositing a thirdsuperconducting material over first superconducting material to form asecond Josephson junction at a second position, wherein the secondJosephson junction comprises a first portion of the firstsuperconducting material, a second portion of third superconductingmaterial, and a second insulating barrier.
 17. The method of claim 16,wherein the method forms a gradiometric superconducting quantuminterference device, and wherein the Josephson junction is asuperconductor-insulator-superconductor Josephson junction that connectsthe first superconducting material and the second superconductingmaterial.
 18. The method of claim 16, wherein the forming the insulatingbarrier comprises oxidizing the first superconducting material.
 19. Themethod of claim 18, wherein the depositing the first superconductingmaterial comprises evaporating the first superconducting material ontothe substrate, and wherein the depositing the second superconductingmaterial comprises evaporating the second superconducting material overthe insulating barrier.
 20. The method of claim 19, wherein the firstsuperconducting material is selected from a first group consisting of atype-1 superconducting material and a type-2 superconducting material,wherein the second superconducting material is selected from a secondgroup consisting of a type-1 superconducting material and a type-2superconducting material, and wherein the insulating barrier is anelectrically insulating dielectric material at low temperature.
 21. Amethod, comprising: forming a first pattern of superconducting materialon a substrate; forming an insulating barrier adjacent to the firstpattern of superconducting material such that the first pattern ofsuperconducting material separates the insulating barrier from thesubstrate; and forming a second pattern of superconducting materialacross the insulating barrier to form a Josephson junction at aposition; forming a third pattern of superconducting material across thefirst pattern of superconducting material to form a second Josephsonjunction at a second position, wherein the second Josephson junctioncomprises a first portion of the first pattern of superconductingmaterial, a second portion of third pattern of superconducting material,and a second insulating barrier.
 22. The method of claim 21, wherein themethod forms a gradiometric superconducting quantum interference device,and wherein the Josephson junction is asuperconductor-insulator-superconductor Josephson junction that connectsthe first pattern of superconducting material and the second pattern ofsuperconducting material.
 23. The method of claim 22, wherein theforming the insulating barrier comprises oxidizing the first pattern ofsuperconducting material.
 24. The method of claim 18, wherein theforming the first superconducting material comprises evaporating thefirst superconducting material onto the substrate, and wherein theforming the second superconducting material comprises evaporating thesecond superconducting material over the insulating barrier.
 25. Themethod of claim 24, wherein the first superconducting material isaluminum, wherein the second superconducting material is aluminum, andwherein the insulating barrier is aluminum oxide.
 26. The method ofclaim 22, wherein the second Josephson junction is a secondsuperconductor-insulator-superconductor Josephson junction.